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116 lines
4.4 KiB
Org Mode
116 lines
4.4 KiB
Org Mode
# -*- coding: utf-8 -*-
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#+TITLE: =ltl2tgta=
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#+DESCRIPTION: Spot command-line tool for translating LTL into Transition-based Generalized Testing Automata.
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#+INCLUDE: setup.org
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#+HTML_LINK_UP: tools.html
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#+PROPERTY: header-args:sh :results verbatim :exports code
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This tool generates various form of Testing Automata, i.e., automata
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that observe the /changes/ of atomic propositions, not their values.
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Three types of automata can be output. The only output format
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supported currently is [[http://www.graphviz.org/][GraphViz]]'s format, with option =-8= to enable
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UTF-8 characters as in other tools.
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The =--ta= option will translate a formula into Testing Automaton, as
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described by [[http://spinroot.com/spin/Workshops/ws06/039.pdf][Geldenhuys and Hansen (Spin'06)]].
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Here is the output on =a U Gb= (we omit the call to =dot=, as shown while
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discussing [[file:ltl2tgba.org][=ltl2tgba=]]).
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#+NAME: augb-ta
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#+BEGIN_SRC sh
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ltl2tgta --ta --multiple-init 'a U Gb'
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#+END_SRC
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#+BEGIN_SRC dot :file augb-ta.svg :var txt=augb-ta :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:augb-ta.svg]]
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As always, the labels of the states have no influence on the language
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recognized by the automaton. This automaton has three possible
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initial states. The initial state should be chosen depending on the
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initial valuation of =a= and =b= in the system to be synchronized with
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this testing automaton. For instance if =a= is true and =b= false in
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the initial state, the testing automaton should start in the state
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pointed to by the initial arrow labeled =a & !b=. In the rest of the
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testing automaton, the transitions are labeled by the sets of atomic
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propositions that should change in the system for the testing
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automaton to progress. States with a double enclosure are Büchi
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accepting, meaning that any execution that visits one of these states
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is accepting. All states have an implicit self-loop labeled by ={}=:
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if the system progress without changing the value of =a= and =b=, the
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testing automaton remains in the same state. Rectangle states are
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livelock-accepting: any execution of the system that get stuck into
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one of these state is accepting.
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Without the =--multiple-init= option, a fake initial state is added.
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This is the default since it often makes the result more readable.
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#+NAME: augb-ta2
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#+BEGIN_SRC sh
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ltl2tgta --ta 'a U Gb'
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#+END_SRC
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#+BEGIN_SRC dot :file augb-ta2.svg :var txt=augb-ta2 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:augb-ta2.svg]]
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The =--gba= option can be used to request a Generalized Testing
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Automaton, i.e., a Testing Automaton with Generalized Büchi
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acceptance. In that case double-enclosures are not used anymore, and
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Büchi accepting transitions are marked with the same ={0,1}=
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notation used in TGBA.
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#+NAME: gfagfb-gta
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#+BEGIN_SRC sh
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ltl2tgta --gta 'GFa & GFb'
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#+END_SRC
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#+BEGIN_SRC dot :file gfagfb-gta.svg :var txt=gfagfb-gta :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:gfagfb-gta.svg]]
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The interpretation is similar to that of the TA. Execution that
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stutter in a livelock-accepting (square) state are accepting as well
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as execution that visit the =0= and =1= acceptance sets
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infinitely often. Those acceptance sets are carried by transitions,
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as in TGBAs.
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Finally, the default is to output a Transition-based Generalized
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Testing Automaton [fn:topnoc]. In TGTAs, the stuttering states are
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made explicit with ={}= self-loops. Since these self-loop can be in
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acceptance sets, livelock acceptance states are no longer needed.
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#+NAME: gfagfb-tgta
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#+BEGIN_SRC sh
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ltl2tgta 'GFa & GFb'
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#+END_SRC
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#+BEGIN_SRC dot :file gfagfb-tgta.svg :var txt=gfagfb-tgta :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:gfagfb-tgta.svg]]
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[fn:topnoc]: This new class of automata, as well as the implementation
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of the previous testing automata classes, is part of Ala Eddine BEN
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SALEM's PhD work, and is discussed in [[https://www.lrde.epita.fr/~adl/dl/adl/bensalem.12.topnoc.pdf][*Model checking using
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generalized testing automata*]], /Ala Eddine Ben Salem/, /Alexandre
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Duret-Lutz/, and /Fabrice Kordon/, in Transactions on Petri Nets and
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Other Models of Concurrency (ToPNoC VI), LNCS 7400, p. 94--112, 2012.
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# LocalWords: ltl tgta num toc Automata automata GraphViz UTF Gb na
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# LocalWords: Geldenhuys tgba SRC init invis nb Acc augb sed png fn
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# LocalWords: cmdline Tpng txt Büchi livelock gba gta GFa GFb TGTAs
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# LocalWords: gfagfb topnoc Eddine SALEM's ToPNoC LNCS eval setenv
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# LocalWords: concat getenv setq utf html args svg TGBAs Alexandre
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# LocalWords: Duret Lutz Fabrice Kordon Petri
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